The reels on your instagram page look very similar to the smaller Armour reels (the one on the right on the picture a bit down on this page:
https://www.smecc.org/wire_recorder_care_&_repair.htm) that were fairly common among many consumer machines such as Webster-Chicago, or the Swedish Luxor. Your reels look like they hove some form of cogs on the inside of the hold though.
I measured the (smaller) Armour standard reels I have, and the outside diameter is 71.3mm, the hole 41mm and the thickness 15.6mm. If this matches the diameter of the spools for the Agaphone it could be that they adopted a standardized spool inside the magazine, which if would make it easier (both then and now) to procure wire.